Question

1. calculate.

(1) \\(1\frac{1}{8} + \frac{5}{8} - \frac{3}{8}\\)
=

(2) \\(1\frac{1}{8} - \frac{3}{8} + \frac{5}{8}\\)
=

(3) \\(2\frac{1}{3} - 1\frac{1}{2} + \frac{3}{4}\\)
=

(4) \\(6\frac{1}{3} - 2\frac{2}{5} + 1\frac{3}{10}\\)
=

note (2) you may change the order as shown below.
\\(1\frac{1}{8} + \frac{5}{8} - \frac{3}{8}\\)

Explanation:

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<reasoning>

Solve sub-questions (1) and (2)

\[

$$\begin{aligned} (1)\quad 1\frac{1}{8} + \frac{5}{8} - \frac{3}{8} &= \frac{9}{8} + \frac{5}{8} - \frac{3}{8} = \frac{14}{8} - \frac{3}{8} = \frac{11}{8} = 1\frac{3}{8}\\ (2)\quad 1\frac{1}{8} - \frac{3}{8} + \frac{5}{8} &= 1\frac{1}{8} + \frac{5}{8} - \frac{3}{8} = 1\frac{3}{8} \end{aligned}$$

\]

Solve sub-question (3)

\[

$$\begin{aligned} (3)\quad 2\frac{1}{3} - 1\frac{1}{2} + \frac{3}{4} &= \frac{7}{3} - \frac{3}{2} + \frac{3}{4}\\ &= \frac{28}{12} - \frac{18}{12} + \frac{9}{12}\\ &= \frac{10}{12} + \frac{9}{12} = \frac{19}{12} = 1\frac{7}{12} \end{aligned}$$

\]

Solve sub-question (4)

\[

$$\begin{aligned} (4)\quad 6\frac{1}{3} - 2\frac{2}{5} + 1\frac{3}{10} &= \frac{19}{3} - \frac{12}{5} + \frac{13}{10}\\ &= \frac{190}{30} - \frac{72}{30} + \frac{39}{30}\\ &= \frac{118}{30} + \frac{39}{30} = \frac{157}{30} = 5\frac{7}{30} \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

\(1\frac{1}{8} + \frac{5}{8} - \frac{3}{8} = 1\frac{3}{8}\)

Question 2

\(1\frac{1}{8} - \frac{3}{8} + \frac{5}{8} = 1\frac{3}{8}\)

Question 3

\(2\frac{1}{3} - 1\frac{1}{2} + \frac{3}{4} = 1\frac{7}{12}\)

Question 4

\(6\frac{1}{3} - 2\frac{2}{5} + 1\frac{3}{10} = 5\frac{7}{30}\)
</answer>

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Answer:

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<reasoning>

Solve sub-questions (1) and (2)

\[

$$\begin{aligned} (1)\quad 1\frac{1}{8} + \frac{5}{8} - \frac{3}{8} &= \frac{9}{8} + \frac{5}{8} - \frac{3}{8} = \frac{14}{8} - \frac{3}{8} = \frac{11}{8} = 1\frac{3}{8}\\ (2)\quad 1\frac{1}{8} - \frac{3}{8} + \frac{5}{8} &= 1\frac{1}{8} + \frac{5}{8} - \frac{3}{8} = 1\frac{3}{8} \end{aligned}$$

\]

Solve sub-question (3)

\[

$$\begin{aligned} (3)\quad 2\frac{1}{3} - 1\frac{1}{2} + \frac{3}{4} &= \frac{7}{3} - \frac{3}{2} + \frac{3}{4}\\ &= \frac{28}{12} - \frac{18}{12} + \frac{9}{12}\\ &= \frac{10}{12} + \frac{9}{12} = \frac{19}{12} = 1\frac{7}{12} \end{aligned}$$

\]

Solve sub-question (4)

\[

$$\begin{aligned} (4)\quad 6\frac{1}{3} - 2\frac{2}{5} + 1\frac{3}{10} &= \frac{19}{3} - \frac{12}{5} + \frac{13}{10}\\ &= \frac{190}{30} - \frac{72}{30} + \frac{39}{30}\\ &= \frac{118}{30} + \frac{39}{30} = \frac{157}{30} = 5\frac{7}{30} \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

\(1\frac{1}{8} + \frac{5}{8} - \frac{3}{8} = 1\frac{3}{8}\)

Question 2

\(1\frac{1}{8} - \frac{3}{8} + \frac{5}{8} = 1\frac{3}{8}\)

Question 3

\(2\frac{1}{3} - 1\frac{1}{2} + \frac{3}{4} = 1\frac{7}{12}\)

Question 4

\(6\frac{1}{3} - 2\frac{2}{5} + 1\frac{3}{10} = 5\frac{7}{30}\)
</answer>

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